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A Large Scale Approach to Decomposition SpacesFeb 20 2019Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces, shearlet spaces ... More

Twisting $c_0$ around nonseparable Banach spacesFeb 20 2019We consider the class of Banach space $Y$ for which $c_0$ admits a nontrivial twisted sum with $Y$. We present a characterization of such space $Y$ in terms of properties of the $weak^\ast$ topology on $Y^\ast$. We prove that under the continuum hypothesis ... More

On the description of normal Hausdorff operators on Lebesgue spacesFeb 20 2019The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some matrix-function (its ... More

On the bi-Lipschitz geometry of lamplighter graphsFeb 19 2019In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes with distortion at most $6$. It follows that lamplighter graphs over countable ... More

Pointwise Multipliers between weighted Copson and Cesàro function spacesFeb 19 2019In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces $\operatorname{Cop}_{p_1,q_1}(u_1,v_1)$ and weighted Ces\`{a}ro function spaces $\operatorname{Ces}_{p_2,q_2}(u_2,v_2)$ is presented, where $p_1,\,p_2,\,q_1,\,q_2 ... More

Extreme contractions on finite-dimensional polygonal Banach spaces-IIFeb 19 2019We introduce the concept of weak L-P property for a pair of Banach spaces, in the study of extreme contractions. We give examples of pairs of Banach spaces (not) satisfying weak L-P property and apply the concept to compute the exact number of extreme ... More

Repeated quasi-integration on locally compact spacesFeb 19 2019When $X$ is locally compact, a quasi-integral (also called a quasi-linear functional) on $ C_c(X)$ is a homogeneous, positive functional that is only assumed to be linear on singly-generated subalgebras. We study simple and almost simple quasi-integrals, ... More

Row contractions annihilated by interpolating vanishing idealsFeb 18 2019We study similarity classes of commuting row contractions annihilated by what we call higher order vanishing ideals of interpolating sequences. Our main result exhibits a Jordan-type direct sum decomposition for these row contractions. We illustrate how ... More

Generalized Bessel and Frame MeasuresFeb 18 2019Considering a finite Borel measure $ \mu $ on $ \mathbb{R}^d $, a pair of conjugate exponents $ p, q $, and a compatible semi-inner product on $ L^p(\mu) $, we introduce $ (p,q) $-Bessel and $ (p,q) $-frame measures as a generalization of the concepts ... More

Functions of noncommuting operators under perturbation of class $\boldsymbol{S}_p$Feb 17 2019In this article we prove that for $p>2$, there exist pairs of self-adjoint operators $(A_1,B_1)$ and $(A_2,B_2)$ and a function $f$ on the real line in the homogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$ such that the differences $A_2-A_1$ and $B_2-B_1$ ... More

The boundedness of a class of fractional type rough higher order commutators on vanishing generalized weighted Morrey spacesFeb 17 2019This paper includes new bounds concepting the vanishing generalized weighted Morrey space. In this sense, it is outlined improved bounds about the a class of fractional type rough higher order commutators on vanishing generalized weighted Morrey spaces. ... More

Constructing Subspace Packings from Other PackingsFeb 17 2019The desiderata when constructing collections of subspaces often include the algebraic constraint that the projections onto the subspaces yield a resolution of the identity like the projections onto lines spanned by vectors of an orthonormal basis (the ... More

Metric currents and polylipschitz formsFeb 16 2019We construct, for a locally compact metric space $X$, a space of polylipschitz forms $\Gamma^*_c(X)$, which is a pre-dual for the space of metric currents of $\mathscr{D}_*(X)$ Ambrosio and Kirchheim. These polylipschitz forms may be seen as a substitute ... More

Re-expansions on compact Lie groupsFeb 16 2019In this paper we consider the re-expansion problems on compact Lie groups. First, we establish weighted versions of classical re-expansion results in the setting of multi-dimensional tori. A natural extension of the classical re-expansion problem to general ... More

Non-linear functionals, deficient topological measures, and representation theorems on locally compact spacesFeb 15 2019We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact spaces. We prove ... More

Antipodal Hadwiger numbers of finite-dimensional Banach spacesFeb 14 2019Let $X$ be a finite dimensional Banach space; we introduce and investigate a natural generalization of the concepts of Hadwiger number $H(X)$ and strict Hadwiger number $H'(X)$. More precisely, we define the antipodal Hadwiger number $H_\alpha(X)$ as ... More

The Strong Maximum Principle for Schrödinger operators on fractalsFeb 14 2019We prove a strong maximum principle for Schr\"odinger operators defined on a class of fractal sets and their blowups without boundary. Our primary interest is in weaker regularity conditions than have previously appeared in the literature; in particular ... More

Topology of Gleason Parts in maximal ideal spaces with no analytic discsFeb 14 2019We strengthen, in various directions, the theorem of Garnett that every sigma-compact, completely regular space X occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its maximal ... More

Topology of Gleason Parts in maximal ideal spaces with no analytic discsFeb 14 2019Feb 15 2019We strengthen, in various directions, the theorem of Garnett that every $\sigma$-compact, completely regular space $X$ occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its ... More

Spectral Action in Noncommutative GeometryFeb 14 2019What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry \`a la Connes, deliberately unveiling the answers to these questions. After a brief ... More

Some Properties of Thinness and Fine Topology with Relative CapacityFeb 14 2019In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely closed sets. We ... More

Generalized subdifferentials of spectral functions over Euclidean Jordan algebrasFeb 14 2019This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems field playing the role of "regularizer", "barrier", "penalty function" and ... More

Remarks on the strict order propertyFeb 14 2019A well-known theorem of Shelah asserts that a theory has $OP$ (the order property) if and only if it has $IP$ (the independence property) or $SOP$ (the strict order property). We give a mild strengthening of Shelah's theorem for classical logic and a ... More

Interpolation between $L_0({\mathcal M},τ)$ and $L_\infty({\mathcal M},τ)$Feb 14 2019Let ${\mathcal M}$ be a semifinite von Neumann algebra with a faithful semifinite normal trace $\tau$. We show that the symmetrically $\Delta$-normed operator space $E({\mathcal M},\tau)$ corresponding to an arbitrary symmetrically $\Delta$-normed function ... More

$L^1$-spaces of vector measures with vector densityFeb 13 2019Let $F$ be a function with values in a Banach space. When $F$ is locally (Pettis or Bochner) integrable with respect to a locally determined positive measure, a vector measure $\nu_F$ with density $F$ defined on a $\delta$-ring is obtained. We present ... More

Embeddings of Orlicz-Lorentz spaces into $L_1$Feb 13 2019In this article, we show that Orlicz-Lorentz spaces $\ell^n_{M,a}$, $n\in\mathbb N$ with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if the norm $\|\cdot\|_{M,a}$ satisfies certain Hardy-type inequalities. ... More

Universal optimality of the $E_8$ and Leech lattices and interpolation formulasFeb 13 2019We prove that the $E_8$ root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions $8$ and $24$, respectively. In other words, they minimize energy for every potential function that is a completely ... More

Entropy numbers of compact embeddings of Smoothness Morrey spaces on bounded domainsFeb 13 2019We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is rather small compared ... More

Zero Jordan product determined Banach algebrasFeb 13 2019A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in A$ are such ... More

Existence of Weak Solutions for $p(.)$-Laplacian Equation via Compact Embeddings of the Double Weighted Variable Exponent Sobolev SpacesFeb 13 2019In this study, we define double weighted variable exponent Sobolev spaces $W^{1,q(.),p(.)}\left( \Omega ,\vartheta _{0},\vartheta \right) $ with respect to two different weight functions. Also, we investigate the basic properties of this spaces. Moreover, ... More

Weighted Stochastic Field Exponent Sobolev Spaces and Nonlinear Degenerated Elliptic ProblemFeb 13 2019In this study, we consider weighted stochastic field exponent function spaces $L_{\vartheta }^{p(.,.)}\left( D\times \Omega \right) $ and $W_{\vartheta }^{k,p(.,.)}\left( D\times \Omega \right) $. Also, we investigate some basic properties and embeddings ... More

The Kolmogorov-Riesz Theorem and Some Compactness Criterions of Bounded Subsets in Weighted Variable Exponent Amalgam and Sobolev SpacesFeb 13 2019We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.

On some properties of relative capacity and thinness in weighted variable exponent Sobolev spacesFeb 13 2019In this paper, we define weighted relative $p(.)$-capacity and discuss properties of capacity in the space $W_{\vartheta }^{1,p(.)}(\mathbb{R}^{n}).$ Also, we investigate some properties of weighted variable Sobolev capacity. It is shown that there is ... More

Asymptotic expansion for the eigenvalues of a perturbed anharmonic oscillatorFeb 12 2019In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise H\"older continuous perturbation and investigate how the H\"older constant can affect the eigenvalues. More precisely, ... More

Gabor windows supported on $[-1,1]$ and construction of compactly supported dual windows with optimal frequency localizationFeb 12 2019We consider Gabor frames $\{e^{2\pi i bm \cdot} g(\cdot-ak)\}_{m,k \in \mathbb{Z}}$ with translation parameter $a=L/2$, modulation parameter $b \in (0,2/L)$ and a window function $g \in C^n(\mathbb{R})$ supported on $[x_0,x_0+L]$ and non-zero on $(x_0,x_0+L)$ ... More

Weighted operator least squares problems and the J-trace in Krein spacesFeb 12 2019Given B, C and W operators in the algebra L(H) of bounded linear operators on the Krein space H, the minimization problem min (BX - C)^#W(BX - C), for X in L(H), is studied when the weight W is selfadjoint. The analogous maximization and min-max problems ... More

Spectral analysis of the Laplacian acting on discrete cusps and funnelsFeb 12 2019We study the Laplacian acting on a discret cusp and a discret funnel. We perturb the metric in a long-range way. Then, we establish a Limiting Absorption Principle away the possible embedded eigenvalues. The approach is based on a positive commutator ... More

Inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$Feb 12 2019We study $L^p$ inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$.

Shadowing and structural stability in linear dynamical systemsFeb 12 2019A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by P. Hartman in 1960 for operators on finite-dimensional spaces. The ... More

A Gleason-Kahane-Żelazko theorem for the Dirichlet spaceFeb 12 2019We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of ... More

Bidual octahedral renormings and strong regularity in Banach spacesFeb 11 2019We prove that every separable Banach space containing $\ell_1$ can be equivalently renormed so that its bidual space is octahedral, which answers, in the separable case, a question by Godefroy in 1989. As a direct consequence, we obtain that every dual ... More

Operator Jensen's inequality for operator superquadratic with applications to quasi-arithmetic meansFeb 11 2019In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed ... More

Direct and inverse limits of normed modulesFeb 11 2019The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.

The Kato square root problem on irregular open setsFeb 11 2019Let $O\subseteq \mathbb{R}^d$ be an open set and $L=-\nabla \cdot A\nabla$ be an elliptic differential operator in divergence form subject to mixed boundary conditions. We show that $L$ possesses the Kato square root property, i.e. the domain of $L^\frac{1}{2}$ ... More

Analogues of Entropy in Bi-Free Probability Theory: MicrostatesFeb 11 2019In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are developed, such as ... More

Analogues of Entropy in Bi-Free Probability Theory: Non-MicrostateFeb 11 2019In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quotients are constructed as analogues of the free partial derivations. Adjoints ... More

Analytic Functional Calculus in Quaternionic FrameworkFeb 11 2019Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions, defined by the ... More

The Positive Maximum Principle on Symmetric SpacesFeb 11 2019We investigate the Courr\`{e}ge theorem in the context of linear operators $A$ that satisfy the positive maximum principle on a space of continuous functions over a symmetric space. Applications are given to Feller--Markov processes. We also introduce ... More

Sharp Cheeger-Buser type inequalities in $ \mathsf{RCD}(K,\infty)$ spacesFeb 11 2019The goal of the paper is to sharpen and generalise bounds involving the Cheeger's isoperimetric constant $h$ and the first eigenvalue $\lambda_{1}$ of the Laplacian. \\A celebrated lower bound of $\lambda_{1}$ in terms of $h$, $\lambda_{1}\geq h^{2}/4$, ... More

An Algorithm for Approximating Continuous Functions on Compact Subsets with a Neural Network with one Hidden LayerFeb 10 2019George Cybenko's landmark 1989 paper showed that there exists a feedforward neural network, with exactly one hidden layer (and a finite number of neurons), that can arbitrarily approximate a given continuous function $f$ on the unit hypercube. The paper ... More

A minimax principle to the injectivity of the Jacobian conjectureFeb 10 2019The main result of this paper is to prove some type of Real Jacobian Conjecture. It is proved by the Minimax Principle and asserts if the eigenvalues of $F'(x)$ are bounded from zero and all the eigenvalues of $F'(x)+F'(x)^T$ are strictly same sign, where ... More

Operator algebras of higher rank numerical semigroupsFeb 10 2019A higher rank numerical semigroup is a positive cone whose seminormalization is isomorphic to the free abelian semigroup. The corresponding nonselfadjoint semigroup algebras are known to provide examples that answer Arveson's Dilation Problem to the negative. ... More

Equivariant homologies for operator algebrasFeb 10 2019This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant theories, such as equivariant $K$-theory and equivariant cyclic homology. As the main focus, we discuss a notion of ... More

lacunary Walsh series in rearrangement invariant spacesFeb 10 2019We prove that the classical results by Rodin and Semenov and by Lindenstrauss and Tzafriri on the subspace generated by the Rademacher system in rearrangement invariant spaces also hold for lacunary Walsh series.

Universal optimal configurations for the $p$-frame potentialsFeb 09 2019Given $d, N\geq 2$ and $p\in (0, \infty]$ we consider a family of functionals, the $p$-frame potentials FP$_{p, N, d}$, defined on the set of all collections of $N$ unit-norm vectors in $\mathbb R^d$. For the special case $p=2$ and $p=\infty$, both the ... More

$m_{n}$-Distributional chaos in Fr\' echet spacesFeb 09 2019The main aim of this paper is to introduce the concepts of $m_{n}$-distributional chaos and $\lambda$-distributional chaos for linear continuous operators and their sequences in Fr\' echet spaces ($\lambda \in (0,1]$), as well as their continuous analogues ... More

Decay and Smoothness for Eigenfunctions of Localization OperatorsFeb 09 2019We study decay and smoothness properties for eigenfunctions of localization operators. Considering symbols in the wide modulation space M^{p,\infty}(R^{2d}) (containing the Lebesgue space L^p(R^{2d})), p < \infty, and two general windows in the Schwartz ... More

Attractors of Trees of Maps and of Sequences of Maps between Spaces with Application to SubdivisionFeb 09 2019In a previous paper we considered a sequence of maps on a complete metric space $(X,d)$ and derived an extension of the Banach fixed point theorem. We showed that backward trajectories of maps $X\to X$ converge under mild conditions and that they can ... More

Quasi-linear functionals on locally compact spacesFeb 09 2019This paper has two goals: to present some new results that are necessary for further study and applications of quasi-linear functionals, and, by combining known and new results, to serve as a convenient single source for anyone interested in quasi-linear ... More

Generalization of Kuratowski problem in linear spacesFeb 08 2019In this short paper, Kuratowski problem will be investigated in vector space. The highest number of distinct sets that can be generated from one convex set in linear space by repeatedly applying algebraic closure and complement in any order is 8. Keywords: ... More

A Note on the Paper "Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps"Feb 08 2019In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend ... More

Quantum Markov States on Cayley treesFeb 08 2019It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-neighbor interactions. In our previous results, we have investigated quantum ... More

Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley treeFeb 08 2019The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QMC) scheme. In this scheme, we employ the $C^*$-algebraic approach to the ... More

Reachability in Infinite Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad GeneratorsFeb 08 2019In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems $\Sigma$ following ... More

Mixed operators on $L^p$-direct integralsFeb 08 2019The notion of decomposable operators acting between different $L^p$-direct integrals of Banach spaces is introduced. We show that those operators generalize the composition operator, in the sense that a mapping is replaced by a binary relation. The necessary ... More

Real Paley-Wiener theorems in spaces of ultradifferentiable functionsFeb 07 2019We develop real Paley-Wiener theorems for classes ${\mathcal S}_\omega$ of ultradifferentiable functions and related $L^{p}$-spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the so-called Gabor transform ... More

A unified factorization theorem for Lipschitz summing operatorsFeb 07 2019We prove a general factorization theorem for Lipschitz summing operators in the context of metric spaces which recovers several linear and nonlinear factorization theorems that have been proved recently in different environments. New applications are ... More

Superposition, reduction of multivariable problems, and approximationFeb 07 2019We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit reductions schemes ... More

A note on Sobolev type inequalities on graphs with polynomial volume growthFeb 07 2019We prove a scale of generalized $L^p$-Poincar\'e inequalities and Sobolev type inequalities on graphs with polynomial volume growth. They are optimal on Vicsek graphs.

Polynomial inequalities on the Hamming cubeFeb 06 2019Let $(X,\|\cdot\|_X)$ be a Banach space. The purpose of this article is to systematically investigate dimension independent properties of vector valued functions $f:\{-1,1\}^n\to X$ on the Hamming cube whose spectrum is bounded above or below. Our proofs ... More

Analyticity of non-symmetric Ornstein-Uhlenbeck semigroup with respect to a weighted Gaussian measureFeb 06 2019In this paper we show that the realization in $L^p(X,\nu_\infty)$ of the nonsymmetric Ornstein-Uhlenbeck operator $L$ is sectorial for any $p\in(1,+\infty)$ and we provide an explicit sector of analyticity. Here $(X,\mu_\infty,H_\infty)$ is an abstract ... More

Stability of the optimal values under small perturbations of the constraint setFeb 06 2019This paper presents a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if we slightly change the constraint set over which the optimal (extreme) values ... More

Sharpening the triangle inequality: envelopes between $L^{2}$ and $L^{p}$ spacesFeb 06 2019Motivated by the inequality $\|f+g\|_{2}^{2} \leq \|f\|_{2}^{2}+2\|fg\|_{1}+\|g\|^{2}_{2}$, Carbery (2006) raised the question what is the "right" analogue of this estimate in $L^{p}$ for $p \neq 2$. Carlen, Frank, Ivanisvili and Lieb (2018) recently ... More

On a problem of PichoridesFeb 06 2019Let $S^{(\Lambda)}$ denote the classical Littlewood-Paley square function formed with respect to a lacunary sequence $\Lambda$ of positive integers. Motivated by a remark of Pichorides, we obtain sharp asymptotic estimates of the behaviour of the operator ... More

On the Operator Equations $A^n=A^*A$Feb 06 2019Let $n\in\mathbb{N}$ and let $A$ be a closed linear operator (everywhere bounded or unbounded). In this paper, we study (among others) equations of the type $A^*A=A^n$ where $n\geq2$ and see when they yield $A=A^*$ (or a weaker class of operators). In ... More

A weighted anisotropic Sobolev type inequality and it's applications to Hardy inequalitiesFeb 06 2019In this paper we focus our attention on an embedding result for a weighted Sobolev space that involves as weight the distance function from the boundary taken with respect to a general smooth gauge function F. Our interest in this type of inequalities ... More

Hardy spaces of general Dirichlet series - a surveyFeb 06 2019The main purpose of this article is to survey on some key elements of a recent $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n e^{-\lambda_{n}s}$, which was mainly inspired by the work of Bayart and Helson on ordinary Dirichlet series $\sum ... More

Gleason parts for algebras of holomorphic functions on the ball of $\mathbf{c_0}$Feb 05 2019For a complex Banach space $X$ with open unit ball $B_X,$ consider the Banach algebras $\mathcal H^\infty(B_X)$ of bounded scalar-valued holomorphic functions and the subalgebra $\mathcal A_u(B_X)$ of uniformly continuous functions on $B_X.$ Denoting ... More

Weighted Translation Semigroups: Multivariable Case-IFeb 05 2019M. Embry and A. Lambert initiated the study of a weighted translation semigroup {S_t}, with a view to explore a continuous analogue of a weighted shift operator. We continued the work, characterized some special types of semigroups and developed an analytic ... More

Stability results of properties related to the Bishop-Phelps-Bollobás property for operatorsFeb 05 2019We prove that the class of Banach spaces $Y$ such that the pair $(\ell_1, Y)$ has the Bishop-Phelps-Bollob\'as property for operators is stable under finite products when the norm of the product is given by an absolute norm. We also provide examples showing ... More

On the geometry of random polytopesFeb 05 2019We present a simple proof to a fact recently established in [5]: let $\xi$ be a symmetric random variable that has variance $1$, let $\Gamma=(\xi_{ij})$ be an $N \times n$ random matrix whose entries are independent copies of $\xi$, and set $X_1,...,X_N$ ... More

Sampling theorem and reconstruction formula for the space of translates on the Heisenberg groupFeb 05 2019The paper deals with the necessary and sufficient conditions for obtaining reconstruction formulae and sampling theorems for every function belonging to the principal shift invariant subspace of $L^2(\mathbb{H}^n)$, both in the time domain and a transform ... More

An explicit formula for preimages of relaxed one-sided Lipschitz mappings with negative Lipschitz constantFeb 04 2019Relaxed one-sided Lipschitz mappings with negative Lipschitz constant are possess a localization property that is stronger than uniform metrical regularity. The present article complements this fact by providing an explicit formula for entire preimages ... More

Weyl-Schrödinger representations of Heisenberg groups in infinite dimensionsFeb 04 2019A complexified Heisenberg's matrix group $\mathrm{H}_\mathbb{C}$ with entries from an infinite-dimensional Hilbert space $H$ and its application to the associated heat equation are considered. The Weyl-Schr\"odinger type irreducible representations of ... More

Stability in Bounded Cohomology for Classical Groups, I: The Symplectic CaseFeb 04 2019We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as $(\mathrm{Sp}_{2r}(\mathbb{Z}))_{r ... More

Estimates of norms of log-concave random matrices with dependent entriesFeb 04 2019We prove estimates for $\mathbb{E} \| X: \ell_{p'}^n \to \ell_q^m\|$ for $p,q\ge 2$ and any random matrix $X$ having the entries of the form $a_{ij}Y_{ij}$, where $Y=(Y_{ij})_{1\le i\le m, 1\le j\le n}$ has i.i.d. isotropic log-concave rows. This generalises ... More

Notes on bilinear multipliers on Orlicz spacesFeb 04 2019Let $\Phi_1 , \Phi_2 $ and $ \Phi_3$ be Young functions and let $L^{\Phi_1}(\mathbb{R})$, $L^{\Phi_2}(\mathbb{R})$ and $L^{\Phi_3}(\mathbb{R})$ be the corresponding Orlicz spaces. We say that a function $m(\xi,\eta)$ defined on $\mathbb{R}\times \mathbb{R}$ ... More

Extreme Singular Values of Random Time-Frequency Structured MatricesFeb 04 2019In this paper, we investigate extreme singular values of the analysis matrix of a Gabor frame $(g, \Lambda)$ with a random window $g$. Columns of such matrices are time and frequency shifts of $g$, and $\Lambda\subset \mathbb{Z}_M\times\mathbb{Z}_M$ is ... More

On switching probability measures and questions of KardarasFeb 03 2019Let $\mathcal{K}$ be a convex bounded positive set in $\mathbb{L}^1(\mathbb{P})$. Kardaras [6] asked the following two questions: (1) If the relative $\mathbb{L}^0(\mathbb{P})$-topology is locally convex on $\mathcal{K}$, does there exist $\mathbb{Q}\sim ... More

Solvability in Gevrey classes of some linear functional equationsFeb 03 2019In this paper, we associate to each positive number k a new class of endomorphisms of the sheaf of germs of holomorphic functions on [-1,1] and prove the solvability in the Gevrey class G_k([-1,1]) of some linear functional equations related to endomorphisms. ... More

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifoldsFeb 03 2019In this paper we investigate Lott-Sturm-Villani's synthetic lower Ricci curvature bound on Riemannian manifolds with boundary. We prove several measure rigidity results for some important functional and geometric inequalities, which completely characterize ... More

Non-harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundaryFeb 03 2019In this paper, following the works on non-harmonic analysis of boundary value problems by Tokmagambetov, Ruzhansky and Delgado, we use Operator Ideals Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential ... More

Spectrality of polytopes and equidecomposability by translationsFeb 03 2019Let $A$ be a polytope in $\mathbb{R}^d$ (not necessarily convex or connected). We say that $A$ is spectral if the space $L^2(A)$ has an orthogonal basis consisting of exponential functions. A result due to Kolountzakis and Papadimitrakis (2002) asserts ... More

SSGP topologies on free groups of infinite rankFeb 03 2019We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity of G, each element g in G can be represented as a product g=g_1 g_2 ... ... More

About a conjecture on difference equations in quasianalytic Carleman classesFeb 02 2019In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.

Ergodic theorems in Banach ideals of compact operatorsFeb 02 2019Let $\mathcal H$ be a complex infinite-dimensional Hilbert space, and let $\mathcal B(\mathcal H)$ ($\mathcal K(\mathcal H)$) be the $C^*$-algebra of bounded (respectively, compact) linear operators in $\mathcal H$. Let $(E,\|\cdot\|_E)$ be a fully symmetric ... More

On the dynamics of a charged particle in magnetic fields with cylindrical symmetryFeb 01 2019We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry axis of the ... More

Deterministic guarantees for $L^{1}$-reconstruction: A large sieve approach with geometric flexibilityFeb 01 2019We present estimates of the $p$-concentration ratio for various function spaces on different geometries including the line, the sphere, the plane, and the hyperbolic disc, using large sieve methods. Thereby, we focus on $L^{1}$-estimates which can be ... More

On some spectral properties of pseudo-differential operators on TJan 31 2019Feb 07 2019In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols in the H\"ormander ... More

On some spectral properties of pseudo-differential operators on TJan 31 2019Feb 14 2019In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols in the H\"ormander ... More